Chapter 3.11, Problem 30P

Let each of the following matrices M describe a deformation of the $\left(x,y\right)$ plane. For each given M find: the eigenvalues and eigenvectors of the transformation, the matrix C which diagonalizes M and specifies the rotation to new axes $\left(x\text{'},y\text{'}\right)$ along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.

$\left(\begin{array}{cc}3& 1\\ 1& 3\end{array}\right)$